RF receivers in general have been designed to convert incoming RF signals into IF signals and then convert IF signals to baseband. FIG. 1 is a diagram illustrating the frequencies of an incoming RF signal, a local oscillator signal and a converted IF signal in prior art. Referring to FIG. 1, a conventional RF receiver may receive an RF signal at a frequency FRF, and convert the RF signal into an IF signal with a nominal intermediate frequency FIF by mixing the received RF signal with a local oscillator (LO) signal centered at FLO=FRF−FIF. Although such a down-conversion can be done in one step with one mixer and one LO, sometimes, the received RF signal is first down-converted to a first IF with a first mixer and a first LO, and then down-converted to the nominal IF at a frequency FIF with a second mixer and a second LO. In what follows, it is assumed that such a RF-to-IF conversion is done in one step. Usually, a channel selection filter such as a band pass filter (BPF) or low pass filter (LPF) may be required to filter out unwanted image and interference signals so as to facilitate a baseband demodulator to detect desired information. The channel selection filter, however, may suffer from an issue of center frequency shift, which can significantly degrade a demodulated signal.
FIG. 2A is a diagram illustrating an exemplary frequency response of a BPF without any center frequency shift. Referring to FIG. 2A, a desirable BPF may have a center frequency FC equal to FIF so that no power deviation may occur between the two nominal half-power points F1 (i.e., the lower 3 dB point) and F2 (i.e., the upper 3 dB point).
However, some BPFs or LPFs may not have a frequency response as illustrated in FIG. 2A. For example, inaccuracy in the frequency response of a BPF may result from deviation in (trans-) conductance-to-capacitance ratio due to process variation and/or environmental temperature change. FIG. 2B is a diagram illustrating an exemplary frequency response of a BPF with a center frequency shift. Referring to FIG. 2B, the center frequency FC′ of the BPF may be offset from FIF by Δf, resulting in, for example, a 20 dB power deviation between the nominal half-power points F1 and F2. To address the issue caused by process variation and/or temperature change, an automatic tuning circuitry may be used to accurately control the filter frequency response, which may inevitably result in design complexity. Such complexity is undesirable, particularly for mobile communications applications where chip size, power consumption and cost per unit must be minimized.